Chapter 7, Problem 71SGR

To determine

The next three terms of the given geometric sequence.

Answer to Problem 71SGR

The next three terms of the geometric sequence are 81, 243, 729.

Explanation of Solution

Given information: The geometric sequence given 3, 9, 27, …

Calculation:

The first term of the geometric sequence is $a_1=3$ .

Second term is $a_2=9$ , third term is $a_3=27$

We know that, common ratio = r = $\frac{a_2}{a_1}=\frac{a_3}{a_2}$ .

  $\therefore r=\frac{9}{3}=\frac{27}{9}=3$

  $\therefore$ The fourth term

  $a_4=a_3\cdot r=27\cdot 3=81$

The fifth term

  $a_5=a_4\cdot r=81\cdot 3=243$

The sixth term

  $a_6=a_5\cdot r=243\cdot 3=729$

  $\therefore$ The next three terms are 81, 243, 729.